Apparatus and method for fixed-frequency control in a switching power supply

ABSTRACT

A sliding-mode switching power supply ( 24 ) having N phases ( 28 ) and a method of operating the power supply ( 24 ) are provided. N switches ( 30 ) are coupled to a bipolar power source ( 22 ), with each switch ( 30 ) effecting one phase ( 28 ). An inductance ( 32 ) is coupled to each switch ( 30 ), and a capacitance ( 36 ) is coupled to the inductances ( 32 ). A load ( 26 ) is coupled across the capacitance ( 36 ). A monitor circuit ( 38 ) is coupled to the inductances ( 32 ) and the capacitance ( 36 ) and configured to monitor currents (I L ) through the inductances ( 32 ) and/or a voltage (V C ) across the capacitance ( 36 ). A sliding-surface generator ( 78 ) is coupled to the monitor circuit ( 38 ) and generates a single sliding surface (σ) for all phases ( 28 ). A constant-frequency control ( 104 ) forms a variable window (Δσ) for the sliding surface (σ). A switching circuit ( 138 ) switches the switches ( 30 ) at a switching frequency (f S ) determined by the variable window (Δσ). The constant-frequency control ( 104 ) adjusts the variable window (Δσ) to maintain the switching frequency (f S ) substantially constant.

RELATED INVENTIONS

The present invention claims benefit under 35 U.S.C. 119(e) to “Switching Power Supply with Sliding-Mode Control,” U.S. Provisional Patent Application Ser. No. 60/588,098, filed 15 Jul. 2004, which is incorporated by reference herein.

The present invention is related to the following U.S. patent applications, each of which was filed on the same date as the present application, is assigned to the assignee hereof, and is incorporated by reference herein:

“Apparatus and Method for Sliding-Mode Control in a Multiphase Switching Power Supply,” by Zaki Moussaoui, Brian L. Allen, and Larry C. Pearce, U.S. Pat. application Ser. No. 10/961,950.

“Apparatus and Method for State-Variable Synthesis in a Switching Power Supply,” by Zaki Moussaoui, U.S. Pat. application Ser. No. 10/961,439; and

“Apparatus and Method for Transient Control in a Multiphase Switching Power Supply,” by Zaki Moussaoui and Thomas Victorin, U.S. Pat. application Ser. No. 10/962,088.

TECHNICAL FIELD OF THE INVENTION

The present invention relates to the field of switching power supplies. More specifically, the present invention relates to the field of switching power supplies that utilize a comprehensive feedback signal and fixed-frequency control.

BACKGROUND OF THE INVENTION

Modern electronic equipment often requires low-ripple, high-current power sources at low to moderate voltages. Conventional switching power supplies can meet these requirements. In addition, switching power supplies are typically more efficient, lighter, and less expensive than their traditional analog counterparts, all of which are advantages in the modern world.

FIG. 1 shows a simplified schematic diagram of a single-phase system 10 utilizing a conventional buck-converter type of switching power supply 11. Power supply 11 incorporates a double-throw switch 12. Switch 12 couples to an inductance 13, and alternately connects a first node of inductance 13 to an input D-C power source 14 and a ground (common) each time switch 12 is toggled. A capacitance 15 and a load 16 are coupled in parallel between a second node of inductance 13 and ground.

Switch 12 is typically realized as a pair of MOSFETs or other active devices operating as double-throw switch 12, and makes a connection in either throw. For the sake of convention, however, this discussion will assume that switch 12 is “on” when it connects inductance 13 to power source 14 and “off” when it connects inductance 13 to ground.

When switch 12 is on, current flows into inductance 13. The energy contained in inductance 13 increases. Current flows from inductance 13 into capacitance 15 and load 16. The energy contained in capacitance 15 also increases. Load 16 receives its energy primarily from inductance 13.

When switch 12 is off, current flows from inductance 13 to ground. The energy contained in inductance 13 decreases. Current flows from capacitance 15 into load 16. Load 16 receives its energy primarily from capacitance 15.

A monitor circuit 17 monitors state variables, such as a voltage across capacitance 15 and a current through inductance 13, to determine when to toggle switch 12. A control circuit 18 controls the switching of switch 12 in response to the state variables monitored by monitor circuit 17.

FIG. 2 shows a simplified schematic diagram of an extension of single-phase system 10 into a multiphase system 10. The following discussion refers to FIG. 2 except as noted therein.

In FIG. 2, system 10 utilizes a multiphase version of switching power supply 11. Often, the high current and/or low ripple requirements of load 16 may be such as to exceed the capabilities of a single switch 12. In such situations, it is common to use N switches 12, where N is an integer greater than one. Each of the N switches 12 couples to its own one of N inductances 13, and connects that one inductance 13 to power source 14 when that switch 12 is on, and to ground when that switch 12 is off. A single power source 14 may be common to all N switches 12. Normally, all inductances 13 couple to a single capacitance 15 and load 16.

Multiphase power supply 11 has N phases 19, where each switch 12 effects one of the N phases 19. Each of the N phases 19 is interleaved with the others. The power dissipated by each switch 12 is a function of the duty cycle of that switch 12. The duty cycle of a given switch 12 is typically maintained at no more than 1/N with N interleaved phases 19. Putting it another way, a symmetrical multiphase system 10 would typically provide approximately N times the current of a single-phase system using the same components for switches 12.

In concept, therefore, there is a significant advantage to multiphase system 10 with a large number of phases 19. However, problems exists with such systems 10 in that, as the number of phases 19 increases, control circuit 18 increases in complexity in order to control and maintain the timing of phases 19. This increase in complexity is reflected in a decrease in reliability and an increase in cost.

One such problem is that each of the N phases 19 should ideally provide approximately the same current. The use of components having typical tolerances may nevertheless result in a wide difference in currents between phases 19, and may result in one switch 12 carrying excessive current. This necessitates that a typical control circuit 18 must manage the individual phase currents, as well as the collective current and the phase timing.

Conventionally, a linear controller is used for control circuit 18. This is a complex circuit requiring inputs from at least N+1 state variables. Moreover, the parameters of a linear controller are tightly matched with the parameters of inductances 13, capacitance 15, and load 16. This often necessitates a change in the controller itself whenever there is even a slight change in inductances 13, capacitance 15, and/or load 16. Consequently, costs associated with control circuit 18 when realized as a linear controller may initially be undesirably high and may be exacerbated by the inability of control circuit 18 to accommodate changes in inductances 13, capacitance 15, and/or load 16.

Control circuit 18 may be realized as a hysteretic controller. Conventional implementations of hysteretic controllers, however, are unsuitable for multiphase systems 10. Even in single-phase systems, hysteretic controllers characteristically exhibit poor performance. This poor performance is due, at least in part, to the inherent lag between the voltage across capacitance 15 and the current through inductances 13. In addition, the switching frequency of switch 12 is dependent upon load 16. That is, the switching frequency will vary as load 16 varies.

Control circuit 18 for system 10 may also be realized as a sliding-mode controller, which may also be viewed as a form of second-order hysteretic controller. Conventional implementations of sliding-mode controllers are also considered unsuitable for multiphase systems 10, but might offer improvements in performance over hysteretic controllers in single-phase systems. With conventional sliding-mode controllers, however, the switching frequency is still dependent upon load 16.

Moreover, simply scaling hysteretic or sliding-mode controllers to manage the phase currents of inductances 13, the collective current, and the phase timing for switches 12 in multiphase system 10 produces no significant improvement in complexity over liner controllers, and does not address the problems of reliability and cost.

Conventional hysteretic and sliding-mode control circuits 18 used in conventional power supplies 11 have switching frequencies that are a function of load 16. That means, as load 16 changes, the switching frequency changes. Since a ripple frequency across capacitance 15, and hence across load 16, is directly related to the switching frequency, changes in load 16 bring about changes in the ripple frequency. The ripple frequency present at load 16 may cause harmonic and/or intermodulation interference with whatever electronic device serves as load 16. Were the ripple frequency to be constant, then the ripple frequency may be chosen to exist in an area of the spectrum to which load 16 is insensitive. Alternatively, relatively simple filtration within load 16 may be used to suppress the effects of the ripple frequency. Allowing ripple frequency to vary makes it difficult to ignore or suppress these effects.

Another problem exists with conventional multiphase switching power supplies utilizing either a hysteretic or sliding-mode control circuit 18 in that, under certain conditions, sudden shifts in load 16 may cause a given switch 12 to enter a lockup condition, i.e., to remain on for an excessive length of time. Under such circumstances, that switch 12 is in danger of exceeding its tolerances and failing. Specifically, the current through that switch 12 for that excessive length of time may cause that switch 12 to exceed its power rating, and may thereby cause a catastrophic failure of that switch 12.

There is a need, therefore, for a switching power supply that has a control circuit that is simple, reliable, and inexpensive, requires a minimal number of state variables, maintains substantially equal current through all inductances, is substantially independent of the tolerances of its components, is immune to variations in the load, is tolerant of switch lockup conditions, and is suitable for either single-phase or multiphase systems.

SUMMARY OF THE INVENTION

Accordingly, it is an advantage of the present invention that an apparatus and method for fixed-frequency control in a switching power supply are provided.

It is another advantage of the present invention that a switching power supply is provided that has a control circuit that is simple, reliable, and inexpensive.

It is another advantage of the present invention that a switching power supply is provided that requires no more than two state variables, regardless of the number of phases.

It is another advantage of the present invention that a switching power supply is provided that is substantially independent of component tolerance.

It is another advantage of the present invention that a power supply is provided that incorporates a control circuit having a switching frequency relatively immune to variations in the load.

It is another advantage of the present invention that a switching power supply is provided that is suitable for either single-phase or multiphase systems.

The above and other advantages of the present invention are carried out in one form by a method of operating a fixed-frequency switching power supply N phases, where N is a positive integer. The method incorporates generating a comprehensive feedback signal from no more than two state variables of the power supply, forming a variable window for the comprehensive feedback signal, translating the comprehensive feedback signal into a stream of switching pulses, switching N switches in response to the stream of switching pulses, and effecting one of the N phases with each of the N switches.

The above and other advantages of the present invention are carried out in another form by a fixed-frequency switching power supply having N phases, where N is a positive integer. The power supply includes N switches configured to be coupled to a bipolar power source, N inductances, wherein each of the N inductances is coupled to one of the N switches, a capacitance coupled to each of the N inductances and configured to be coupled across a load, a feedback-signal generator coupled to the capacitance and configured to generate a comprehensive feedback signal in response to from no more than two state variables of the power supply, a pulse-width-modulation (PWM) generator coupled to the comprehensive feedback-signal generator and configured to translate the feedback signal into a stream of switching pulses at a substantially constant switching frequency, and a phase selector coupled to the N switches, coupled to the PWM generator, and configured to switch the N switches at the substantially constant switching frequency in response to the stream of switching pulses so that each of the N switches effects one of the N phases.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete understanding of the present invention may be derived by referring to the detailed description and claims when considered in connection with the Figures, wherein like reference numbers refer to similar items throughout the Figures, and:

FIG. 1 shows a simplified schematic diagram of a single-phase system utilizing a prior-art switching power supply;

FIG. 2 shows a simplified schematic diagram of a an extension of the prior-art system of FIG. 1 into a multiphase system;

FIG. 3 shows a simplified schematic diagram of a single-phase or multiphase system in accordance with a preferred embodiment of the present invention;

FIG. 4 shows a block diagram of a monitor circuit for the power supply of FIG. 3 in accordance with a preferred embodiment of the present invention;

FIG. 5 shows a block diagram of a control circuit for the power supply of FIG. 3 in accordance with a preferred embodiment of the present invention;

FIG. 6 shows a phase plot depicting a sliding surface and a variable window therefor in accordance with a preferred embodiment of the present invention; and

FIG. 7 shows a chart depicting the switching of each of N switches for the N phases of the power supply of FIG. 3 in accordance with a preferred embodiment of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 3 shows a simplified schematic diagram of a multiphase system 20 including a D-C power source 22 coupled to a switching power supply 24, which is coupled to a load 26. The following discussion refers to FIG. 3.

System 20 is made up of power source 22, power supply 24, and load 26. Power source 22 is configured to provide D-C energy in a first form as input energy to power supply 24. This input energy consists of an input voltage V_(In) at an input current I_(In). Power source 22 may be a battery, an A-C to D-C converter, a solar array, a generator, an alternator, or any other source of suitable D-C energy.

Load 26 demands D-C energy in a second form as output energy from power supply 24. This output energy consists of an output voltage V_(Out) at an output current I_(Out). Load 26 may be any electronic device, but is often a computing device or a communications device, e.g., a computer, a communications satellite, cellular equipment, or the like.

Power supply 24 is coupled between power source 22 and load 26, and is configured to convert D-C energy from the first form supplied by power source 22 into the second form required by load 26.

The parameters of load 26 may change, often abruptly, and often significantly. For example load 26 may be or include a computer having a processor demanding a significant current, as well as auxiliary devices, e.g., a motor and/or a subprocessor, either of which also demands significant current, and either or both of which may be instantaneously activated or deactivated to fulfill a given task. Such changes may result in transients, i.e., abrupt and significant shifts in output current I_(Out). Being abrupt, these transients affect output current I_(Out) dynamically (i.e., during the change) and statically (after the change). From a dynamic (A-C) perspective, load 26 may be said to have an impedance Z, where the dynamic value of output current I_(Out) at a given instant is:

$\begin{matrix} {I_{Out} = {\frac{V_{Out}}{Z}.}} & (1) \end{matrix}$ From a static (D-C) perspective, impedance Z includes a resistance R, where the static value of output current I_(Out) at a given time is:

$\begin{matrix} {I_{Out} = {\frac{V_{Out}}{R}.}} & (2) \end{matrix}$

Those skilled in the art will appreciate that, since it is often nearly impossible to predict the energy demands of load 26 for any given point in time, power source 22 and power supply 24 are normally designed to meet a range of output energy demands, from a predetermined minimum to a predetermined maximum, thereby encompassing the requirements of load 26.

In the preferred embodiment, power supply 24 is a sliding-mode switching power supply 24 (i.e., a second-order hysteretic switching power supply) configured to receive D-C input voltage V_(In) from power source 22 and to supply D-C output voltage V_(Out) to load 26.

Power supply 24 is configured to divide input voltage V_(In) into N phases 28, where N is a positive integer. System 20 includes a single-phase system 20 when N=1 and a multiphase system 20 when N>1. System 20 is assumed to have at least one phase 28. Power supply 24 contains N switches 30, where each switch 30 effects one of the N phases 28. The N switches 30 are coupled to N inductances 32 in a one-to-one correspondence. Each switch 30 alternately connects its particular inductance 32 between power source 22 and a common or ground 34. All N inductances 32 couple to a capacitance 36. Load 26 couples to the N inductances 32 and across capacitance 36.

Switches 30 are typically realized as pairs of MOSFETs or other active devices operating as double-throw switches 30, and make connections in either throw. For the sake of convention, however, this discussion will assume that a given switch 30 is “on” when it connects its inductance 32 to power source 22 and “off” when it connects its inductance 32 to ground 34.

FIG. 4 shows a block diagram of a monitor circuit 38 in accordance with a preferred embodiment of the present invention. The following discussion refers to FIGS. 3 and 4.

FIG. shows a block diagram of a monitor circuit 38 in accordance with a preferred embodiment of the present invention. The following discussion refers to FIGS. 3 and 4.

In the preferred embodiment, monitor circuit 38 is coupled to each of the N inductances 32 and to capacitance 36. Monitor circuit 38 monitors state variables for power supply 24. As a minimum, monitor circuit 38 monitors a capacitive voltage V_(C) (i.e., a voltage across capacitance 36). Since capacitance 36 is coupled directly across load 26, capacitive voltage V_(C) is also output voltage V_(Out).

If, as in the preferred embodiment, monitor circuit 38 monitors nothing more than output voltage V_(Out), monitor circuit 38 may be implemented as nothing more than a conductor coupling capacitance 36 to a control circuit 40. In alternative embodiments, however, monitor circuit 38 may include sensing devices, shown as dotted-line circles in FIG. 4, to monitor inductive currents I_(L1) through I_(LN) flowing through each of inductances 32, a capacitive current I_(C) flowing through capacitance 36, or output current I_(Out) flowing through load 26.

FIG. 5 shows a block diagram of control circuit 40 configured in accordance with a preferred embodiment of the present invention. The following discussion refers to FIGS. 3, 4, and 5.

Control circuit 40 incorporates a first state-variable generator 42, a second state-variable generator 44, a feedback-signal generator 46, a pulse-width-modulation (PWM) generator 48, and a phase selector 50. Optionally, a transient control 52 may be included in some embodiments. Each of these components of control circuit 40 is discussed in detail hereinafter.

Control circuit 40 causes power supply 24 to provide output voltage V_(Out) and output current I_(Out) required by load 26. This is accomplished by controlling the timing of the outputs 54 of phase selector 50, which couple to the N switches 30. Control circuit 40 therefore controls the switching of the N switches 30 to produce the N phases 28.

In a preferred embodiment, control circuit 40 receives output voltage V_(Out), which is also capacitive voltage V_(C), from monitor circuit 38. Output voltage V_(Out) is routed to first state-variable generator 42.

Within first state-variable generator 42, output voltage V_(Out) is subtracted from a reference voltage V_(Ref) by a subtraction circuit 56. Subtraction circuit 56 may be implemented as a simple difference amplifier, though this is not a requirement of the present invention.

Desirably, reference voltage V_(Ref) is a constant value during normal operation, and is equal to the desired voltage to be produced by power supply 24. Reference voltage V_(Ref) need supply only a small amount of current, and can therefore be easily generated to a desired accuracy using a wide variety of techniques well known to those skilled in the art.

An output of subtraction circuit 56 is the difference between reference voltage V_(Ref) and output voltage V_(Out). The output of subtraction circuit 56 is therefore an analog error voltage V_(E) that represents a difference between output voltage V_(Out) (the actual output voltage) and reference voltage V_(Ref) (the desired output voltage). Thus, during normal operation any deviation of output voltage V_(Out) from reference voltage V_(Ref) represents an error from the desired voltage in the amount of the deviation.

An analog-to-digital (A/D) converter 58 then converts analog error voltage V_(E) into a digital error voltage x₁: x ₁ =V _(E) =V _(Out) −V _(Ref).  (3) This digital error voltage x₁ is a first (voltage) state variable x₁ of power supply 24.

It will be appreciated by those skilled in the art that in alternative embodiments other signals from monitor circuit 38 may be routed to first state-variable generator 42 for processing in other manners not discussed herein. These embodiments are represented by a dotted line 60 in FIG. 5. Such an alternative signal may correspond to output current I_(Out) flowing through load 26, correspond to capacitive current I_(C) flowing through capacitance 36, or independently correspond to inductive currents I_(L1) through I_(LN) flowing in one or more of inductances 32. The use of these or other alternative signals does not depart from the spirit of the present invention. In the preferred embodiment, however, collective and individual inductive currents are estimated from first state variable x₁, as discussed in more detail hereinafter.

In the preferred embodiment, A/D converter 58 is a small (4-bit), fast (50 MHz) converter. This is a simple and inexpensive approach. Those skilled in the art will appreciate that other A/D converters may be used without departing from the spirit of the present invention.

Subsequent to A/D converter 58, the circuits and functions of control circuit 40 may be implemented using digital hardware logic and/or microprocessor circuits, the design and logic of which can vary widely from application-to-application but which can be readily adapted by those skilled in the digital electronic arts.

In the preferred embodiment, first state variable x₁, derived from output voltage V_(Out), is the only state variable that needs to be derived directly from a physically monitored parameter of power supply 24. Any other state variable is derived by calculation from first state variable x₁.

First state variable x₁ is output from first state-variable generator 42 and routed to second-state-variable generator 44 and feedback-signal generator 46. Within second state-variable generator 44, first state variable x₁ passes to an inductive-current generator 62. Inductive-current generator 62 calculates a second state variable x₂ as an error rate x₂ (i.e., a rate of error voltage x₁) by extracting the derivative of first state variable x₁ over time:

$\begin{matrix} {x_{2} = {\frac{\mathbb{d}x_{1}}{\mathbb{d}t} = {\frac{\mathbb{d}V_{Out}}{\mathbb{d}t} = {\frac{I_{C}}{C}.}}}} & (4) \end{matrix}$ This is equivalent to taking the derivative of output voltage V_(Out) over time, and is substantially equal to capacitive current I_(C) divided by a value C of capacitance 36.

Inductive-current generator 62 also derives signals representing each of inductive currents I_(L1) through I_(LN), which signals are effectively synthesized inductive currents. Inductive-current generator 62 derives a first synthesized inductive current representing a first inductive current I_(L1) through a first inductance 32′ during a first phase 28′, a second synthesized inductive current representing a second inductive current I_(L2) through a second inductance 32″ during a second phase 28″, and so on through an N^(th) synthesized inductive current representing an N^(th) inductive current I_(LN) through an N^(th) inductance 32 ^(N) during an N^(th) phase 28 ^(N). Each synthesized inductive current represents one of the N inductive currents I_(L1) through I_(LN). Therefore, this discussion refers to either synthesized or physical inductive currents as inductive currents I_(L1) through I_(LN).

Inductive-current generator 62 may receive a signal from phase selector 50 (discussed hereinafter) to identify the currently active phase 28.

Those skilled in the art will appreciate that it is not necessary for inductive-current generator 62 to generate signals that equal inductive currents I_(L1) through I_(LN) as long as the signals generated bear the same relationships to each other as do inductive currents I_(L1) through I_(LN).

In an alternative embodiment, inductive current generator 62 may directly receive one or more of inductive currents I_(L1) through I_(LN) from A/D converter 58, or may associate output current I_(Out) with the currently active phase 28 to parse out inductive currents I_(L1) through I_(LN) for each phase 28.

Feedback-signal generator 46 generates a single feedback signal σ. Moreover, feedback-signal generator 46 produces single feedback signal σ from no more than two state variables of power supply 24, error voltage x₁ and error rate x₂. In the preferred embodiment, single feedback signal σ controls all N phases 28. Accordingly, single feedback signal σ is a comprehensive feedback signal σ because it influences all N phases 28 of multiphase power supply 24.

FIG. 6 shows a phase plot depicting a sliding surface σ and a variable window Δσ therefor in accordance with a preferred embodiment of the present invention. The following discussion refers to FIGS. 3, 4, 5, and 6.

In the preferred embodiment, feedback-signal generator 46 within control circuit 40 is a sliding-surface generator 78 that generates comprehensive feedback signal σ in the form of a single sliding surface σ. By generating comprehensive feedback signal σ as single sliding surface σ, the number of state variables required by feedback-signal generator 46 may be kept to a minimum (i.e., two: one monitored, one calculated) regardless of the number N of phases 28. This small number of state variables is desirable because it leads away from the rapidly expanding complexity encountered in conventional multiphase power supplies that monitor N+1 state variables to control N phases 28. The use of a small number of state variables therefore improves reliability and decreases expense over traditional methodologies.

Hereinafter in this discussion, feedback-signal generator 46 and feedback signal σ are referred to as sliding-surface generator 78 and sliding surface σ, respectively. Sliding-surface generator 78 is discussed in more detail hereinafter.

FIG. 6 depicts the state variables as error voltage x₁ on the horizontal axis and error rate x₂ (i.e., synthesized current) on the vertical axis. As such, FIG. 6 depicts the operation of power supply 24 as defined by its state variables x₁ and x₂. Two spirals are depicted on the horizontal axis, with one spiral centered about a positive value where: x ₁ =V _(Out) −V _(Ref), x₂=0,  (5) and another spiral centered around a negative value where: x ₁ =−V _(Ref), x₂=0.  (6) The positive-value spiral depicts an exemplary track state variables x₁ and x₂ might follow if switches 30 were continuously on, and the negative-value spiral depicts an exemplary track state variables x₁ and x₂ might follow if switches 30 were continuously off. Of course, switches 30 are neither continuously on nor continuously off, but are switched on and off with the goal of maintaining a value of the state variables where: x₁=0, x₂=0.  (7) It is a task of sliding-surface generator 78 to identify when such switching should take place, although sliding surface σ generated by sliding-surface generator 78 may be adjusted as discussed herein by a current-balance control 80 and a variable-window generator 82.

Sliding-mode controls are known to those skilled in the art. Sliding-surface generator 78 is a sliding-mode control that has been adapted for use with power supply 24. In the preferred embodiment, sliding-surface generator 78 generates single sliding surface σ as a function: σ=α·x ₁ +x ₂,  (8) where α is a constant. First state variable (error voltage) x₁ is a monitored voltage state variable, and second state variable (error rate) x₂ is a derived (synthesized) current state variable.

The goals used in establishing this relationship are known to those skilled in the art of sliding-mode controls. In general, error voltage x₁, error rate x₂ (the rate of change of error voltage x₁ over time), and even the acceleration of error voltage x₁ in time may all be taken into account in defining sliding surface σ. Of course, those skilled in the art will appreciate that sliding surface σ is an idealized result. In practice, the state of power supply 24 will seldom be precisely on sliding surface σ. Rather, switches 30 are controlled so that future operation of power supply 24 will, (except for the operations of current-balance control 80 and variable-window generator 82), be directed toward sliding surface σ and the origin of the phase plot shown in FIG. 6. By thus controlling the activation and deactivation of switches 30, the operation of power supply 24, as demonstrated by its state variables x₁ and x₂, will tend to “slide” along sliding surface σ.

In the preferred embodiment, constant σ has a range:

$\begin{matrix} {{0 \leq \alpha \leq \frac{1}{\tau}},} & (9) \end{matrix}$ where τ is a time constant: τ=R·C,  (10) where C is the value of capacitance 36 and R is the resistance of load 26 (i.e., the resistive component of load impedance Z).

As discussed hereinbefore in conjunction with equations (3) and (4), first state variable (error voltage) x₁ represents a difference between output voltage V_(Out), and reference voltage V_(Ref), and second state variable (error rate) x₂ represents a rate of change of first state variable x₁ and is the derivative thereof.

By physically measuring only first state variable x₁ and simulating second state variable x₂ from first state variable x₁, only a single sliding surface (comprehensive feedback signal) σ is required to control any number N of phases 28. Moreover, by refraining from physically measuring a current state variable, no lossy current-measuring devices are required. This further improves reliability and decreases cost in addition to improving efficiency.

Sliding-surface generator 78 generates sliding surface σ, a signal that summarizes and describes the operating state of power supply 24. Those skilled in the art will appreciate that sliding surface σ may also be called a sliding or switching line, curve, plane, or hyperplane in other sliding-mode control applications.

PWM generator 48 is coupled to feedback-signal generator 46. PWM generator 48 is configured to translate single sliding surface σ into a PWM signal 84 consisting of a stream of switching pulses 86. Phase selector 50 (discussed hereinafter) routes different switching pluses 86 within PWM signal 84 to different switches 30.

The following discussion refers to FIGS. 3 and 5.

Within PWM generator 48, optional current-balance control 80 adjusts sliding surface σ and alters it into an adjusted sliding surface σ′. Current-balance control 80 receives signals from inductive-current generator 62 corresponding to inductive currents I_(L1) through I_(LN) flowing in each of inductances 32.

Current-balance control 80 receives inputs that correspond to the N inductive currents I_(L1) through I_(LN) for each phase 28. For an M^(th) one of the N phases 28, where M is an integer in the range 1≦M≦N, the M^(th) inductive current I_(LM) is a current through an M^(th) one of the N inductances 32 coupled to an M^(th) one of the N switches 30 effecting the M^(th) phase 28. Since the M^(th) inductive current I_(LM) is germane only to the M^(th) phase 28, the M^(th) inductive current I_(LM) is a phase current for that M^(th) phase 28.

It is desirable that all of the N inductive currents I_(L1) through I_(LN) be substantially equal so that power supply 24 can supply the maximum current within the capacity of a given set of switches 30, thereby maximizing overall efficiency and reliability. Current-balance control 80 computes a summary statistic I_(X) (not shown) as a reference current for the N inductive currents I_(L1) through I_(LN). In the preferred embodiment, summary statistic I_(X) is desirably an arithmetic mean of the N inductive currents I_(L1) through I_(LN):

$\begin{matrix} {I_{X} = {\frac{I_{L1} + I_{L2} + \ldots + I_{L\; N}}{N}.}} & (11) \end{matrix}$ Those skilled in the art will appreciate that this is not a requirement of the present invention, and that summary statistic I_(X) may be other than the arithmetic mean without departing from the spirit of the present invention.

For each phase 28, current-balance control 80 then computes an error current I_(E) (not shown) as a difference between summary statistic I_(x) and an inductive current I_(L) for that phase 28: I _(E) =I _(Ref) −I _(L).  (12) For each M^(th) phase 28, current-balance control 80 then alters sliding surface σ into adjusted sliding surface σ′ so that inductive current I_(L) for that phase 28 is substantially equal to summary statistic I_(X).

In particular, current-balance control 80 adds an offset proportional to error current I_(E) (not shown) to sliding surface σ when a given phase 28 has been providing inductive current I_(L) not equal to summary statistic I_(X). The provided offset will make adjusted sliding surface σ′ slightly different from sliding surface σ, and the operation of power supply 24 for that phase 28 will slide along adjusted sliding surface σ′. In this manner, all phase currents I_(L1) through I_(LN) are rendered substantially equal.

Current-balance control 80 is a desirable but optional component in control circuit 40. This discussion assumes the presence of current-balance control 80. If current-balance control 80 is omitted, then sliding surface σ is not adjusted to become adjusted sliding surface σ′, and any mention of sliding surface σ hereinafter also applies to adjusted sliding surface σ′.

The following discussion refers to FIGS. 3, 5, and 6.

Adjusted sliding surface σ is routed to a translation circuit 102 configured to convert adjusted sliding surface σ′ into PWM signal 84, wherein PWM signal 84 consists of a stream of switching pulses 86 at substantially a switching frequency f_(S).

Variable-window generator 82 is configured to compare sliding surface σ to two offset values. In particular, variable-window generator 82 bifurcates sliding surface σ. Whenever operation greater than a high threshold 106 of sliding surface σ is detected, variable-window generator 82 activates, causing a switch 30 to switch on. This effects one of the N phases 28. Whenever operation less than a low threshold 108 of sliding surface σ is detected, variable-window generator 82 deactivates, causing the currently active switch 30 to switch off. Those skilled in the art will appreciate that other methodologies for the operation of variable-window generator 82 may be used without departing from the spirit of the present invention.

FIG. 6 also depicts an exemplary oscillating sliding signal 110 between the limits of high threshold 106 and low threshold 108. Sliding signal 110 depicts the operation of power supply 24, as defined by its state variables x₁ and x₂, as it slides along sliding surface σ. Oscillation results from switching switches 30 at switching frequency f_(S). Thus, the oscillation frequency of sliding signal 110 tracks switching frequency f_(S).

Switching frequency f_(S) produces a ripple frequency f_(R) across capacitance 36, and therefore across load 26. It is desirable that ripple frequency f_(R) be substantially fixed or constant so that any interference and/or harmonic effects produced thereby may more easily be suppressed within the electronic device serving as load 26. A constant predetermined frequency f_(P) (not shown) serves as an ideal or target ripple frequency f_(R). That is, power supply 24 in general, and constant-frequency control 104 in particular, maintain switching frequency f_(S), and therefore ripple frequency f_(R), substantially equal to constant predetermined frequency f_(P).

Within translation circuit 102, a reference generator 112 generates a fixed reference frequency f_(X), and a frequency comparator 114 compares switching frequency f_(S) against reference frequency f_(X) to produce a frequency error E_(f). In the preferred embodiment, reference generator 112 provides fixed reference frequency f_(X) as a clock signal exhibiting a frequency much greater than the expected switching frequency f_(S). Frequency comparator 114 counts reference frequency f_(X) for a predetermined number of cycles of switching frequency f_(S). The resultant count then becomes frequency error E_(f). As shown in FIG. 6, an increase in the count indicates a decrease in switching frequency f_(S), shown as a frequency-decreasing direction (arrow) 116 and a decrease in the count indicates an increase in switching frequency f_(S), shown as a frequency-increasing direction (arrow) 118. Those skilled in the art will appreciate that other methodologies may be used to determine frequency error E_(f). The use of another methodology does not depart from the spirit of the present invention.

Frequency error E_(f) is applied to variable-window generator 82. Variable-window generator 82 forms and/or adjusts variable window Δσ in response to frequency error E_(f). In the preferred embodiment, frequency error E_(f) is scaled by an appropriate multiplier and added to a constant corresponding to the desired predetermined constant frequency to produce an offset. The offset thus produced increases when an increase 118 in switching frequency f_(S) is detected, and vice-versa. Those skilled in the art will appreciate that other methodologies for adjusting variable window Δσ may be used without departing from the spirit of the present invention.

Constant-frequency control 104 maintains switching frequency f_(S) substantially equal to predetermined constant frequency under static conditions. Unfortunately, conditions are dynamic, not static. Load 26 exhibits changes, sometimes abruptly, and sometimes significantly. Switching frequency f_(S) is dependent not only upon variable window Δσ, but also upon the demands of load 26. Specifically, if impedance Z (i.e., resistance R) of load 26 changes, output current I_(Out) changes and switching frequency f_(S) is urged to change.

When load 26 exhibits a change, output current I_(Out) instantly changes as well. The change in output current I_(Out) produces a first marginal change in switching frequency f_(S). The first marginal change may be in frequency-increasing direction 116 for an increase in output current I_(Out) or a frequency-decreasing direction 118 for a decrease in output current I_(Out). The degree or amount of change is not relevant for the purposes of this discussion. Frequency comparator 114 compares the marginally changed switching frequency f_(S) against reference frequency f_(X) and produces frequency error E_(f) reflecting the change in switching frequency f_(S). Constant-frequency control 104 then adjusts variable window Δσ accordingly by means of an offset to sliding surface σ. This adjustment produces a second marginal change in switching frequency f_(S) in opposition to the first marginal change. In other words, if the first marginal change was in frequency-decreasing direction 118, then the second marginal change will be in frequency-increasing direction 116, and vice-versa. This second marginal change causes switching frequency f_(S) to become more closely equal to the desired predetermined constant frequency.

Those skilled in the art will appreciate that the second marginal change need not completely offset the first marginal change. Indeed, to compensate for the first marginal change in a single step is contrary to accepted negative feedback practice and may lead to instability. Successive iterations of the process are normally used, where each iteration renders switching frequency f_(S) more closely equal to the desired predetermined constant frequency. This practice will rapidly bring and maintain switching frequency f_(S) into substantial equality with the desired predetermined constant frequency.

Constant-frequency control 104 will maintain switching frequency f_(S) substantially constant. Those skilled in the art will appreciate that it need not maintain perfect constancy but desirably maintains substantial constancy within a reasonable tolerance about predetermined constant frequency.

Transients may occur in response to sudden and/or significant changes in load 26. Under certain conditions, these transients may drive power supply 24 into a lockup condition for an undesirably long duration. Eventually, the lockup condition will clear, even when inductances 32, capacitance 36, and/or load 26 are vastly mismatched and/or vary widely from design ideals.

During such a transient, feedback-signal generator 46 may output sliding surface σ that might, when further processed by translation circuit 102, instruct the switch 30 effecting the currently active phase 28 to remain in its on condition. This is may lead to a failure of that switch 30, and is therefore undesirable.

PWM signal 84 is output from PWM generator 48, and input to an optional transient control 52. Within transient control 52, PWM signal 84 is modified to become a modified PWM signal 124. Modified PWM signal 124 is configured to regulate a duration of a lockup condition of any given switch 30 due to a transient from load 26. By regulating the duration of a lockup condition, transient control 52 inhibits potential damage to that switch 30, and to power supply 24.

In the event of a lockup condition, transient control 52 causes the currently active phase 28 to terminate and the next phase 28 to commence after a predetermined duration. In other words, switches 30 are switched from the currently active phase 28 to the next phase 28. Lockup conditions are thereby tolerated.

Transient control 52 is a desirable but optional component in control circuit 40. This discussion assumes the presence of transient control 52, and that PWM signal 84 becomes modified PWM signal 124. If transient control 52 is omitted, then PWM signal 84 is not modified, i.e., modified PWM signal 124 is PWM signal 84.

FIG. 7 shows a chart depicting the distribution and switching of switching pulses 86 to each of switches 30 for the N phases 28 in accordance with a preferred embodiment of the present invention. For the sake of simplicity, FIG. 7 assumes N phases 28 where N=3 (i.e., three phases 28). Those skilled in the art will appreciate that this is exemplary only, applies only to multiphase systems 20, and that N may be any desired integer greater than one. The following discussion refers to FIGS. 3, 4, 5, and 7.

Within phase selector 50, PWM signal 84 is routed to a phase counter 136. Phase counter 136 identifies which of the N phases 28 is to be active at any given point in time. Desirably, phase counter 136 “counts” once for each switching pulse 86 in PWM signal 84, cycling as required. For example, in a three-phase application (i.e., where N=3, as in FIG. 7), phase counter 136 may count from zero to two, then on the receipt of the next switching pulse from PWM signal 84 be reset back to zero.

In the preferred embodiment, phase counter 136 is realized as a ring counter. Those skilled in the art will appreciate that this is not a requirement of the present invention, and that other embodiments of phase counter 136 may be used without departing from the spirit of the present invention.

Output from phase counter 136 are provided to a switching circuit 138, as well as to inductive-current generator 62 and to current-balance control 80 as discussed hereinbefore. This allows inductive-current generator 62 and current-balance control 80 to coordinate their activities with the currently active phase 28.

Switching circuit 138 sequentially distributes switching pulses 86 from PWM signal 84 to the control inputs of the N switches 30. Accordingly, the output from phase counter 136 identifies the target switch 30 to be switched on or off, and PWM signal 84 provides the timing for the switch-on and switch-off events. Signals 54 from switching circuit 138 couple to control inputs of each of switches 30 in each of phases 28. That is, a first signal 54′ is coupled to the control inputs of a first switch 30′ to effect first phase 28′, a second signal 54″ is coupled to the control inputs of a second switch 30″ to effect second phase 28″, and so forth until an N^(th) signal 54 ^(N) is coupled to the control inputs of an N^(th) switch 30 ^(N) to effect the N^(th) phase 28 ^(N).

Collectively, switches 30 then switch at switching frequency f_(S). For an M^(th) one of the N phases 28, switching circuit 138 switches from an M^(th) to an (M+1)^(th) switch 30 under the control of phase counter 136.

In a multiphase power supply 24 (i.e., when N>1), as in the preferred embodiment, switching circuit 138 may be implemented using a relatively simple decoding circuit (not shown) well known to those skilled in the art. It will be appreciated, however, that alternative implementations of switching circuit 138 may be used without departing from the spirit of the present invention.

Those skilled in the art will appreciate that for a single-phase power supply 24 (i.e., when N=1), transient control 52 and phase counter 136 may be omitted. In this situation, switching circuit 138 may be implemented using conductors or buffering circuits which route PWM signal 84 to the control inputs of switch 30 for that single phase 28.

In summary, the present invention teaches an apparatus and method for fixed-frequency control in a switching power supply 24. Power supply 24 has a control circuit 40, suitable for either single-phase or multiphase systems 20, that is simple, reliable, and inexpensive, and requires only two state variables x₁ and x₂, regardless of the number N of phases 28. Power supply 24 is substantially independent of component tolerance, is tolerant of lockup conditions of switches 30, and has a switching frequency f_(S) relatively immune to variations in load 26.

Although the preferred embodiments of the invention have been illustrated and described in detail, it will be readily apparent to those skilled in the art that various modifications may be made therein without departing from the spirit of the invention or from the scope of the appended claims. 

1. A method of operating a fixed-frequency switching power supply having N phases, where N is a positive integer, said method comprising: generating a comprehensive feedback signal from no more than two state variables of said power supply; forming a variable window for said comprehensive feedback signal; translating said comprehensive feedback signal into a stream of switching pulses; switching N switches in response to said stream of switching pulses; and effecting one of said N phases with each of said N switches.
 2. A method as claimed in claim 1 additionally comprising: monitoring an output voltage of said power supply; deriving a first state variable of said power supply in response to said monitoring activity; and synthesizing a second state variable of said power supply in response to said deriving activity.
 3. A method as claimed in claim 2 wherein said deriving activity comprises: generating a fixed reference voltage; subtracting said output voltage from said fixed reference voltage to derive said first state variable.
 4. A method as claimed in claim 2 wherein said synthesizing activity comprises: extracting a derivative of said first state variable over time to synthesize said second state variable.
 5. A method as claimed in claim 1 wherein said generating activity generates said comprehensive feedback signal as a single sliding surface for said N phases, said sliding surface having a value αx₁+x₂, where: α is a constant greater than 0; x₁ is a first state variable of said power supply; and x₂ is a second state variable of said power supply. second state variable corresponding to a rate of change of said first state variable.
 6. A method as claimed in claim 1 additionally comprising: generating signals corresponding to said N inductive currents in response to said monitoring activity, wherein said signals are N synthesized inductive currents; and adjusting said comprehensive feedback signal for each of said N phases so that said N synthesized inductive currents are rendered more closely equal.
 7. A method as claimed in claim 1 additionally comprising: producing a first marginal change in said switching frequency in response to a change in said load; adjusting said variable window in response to said producing activity; and producing a second marginal change in said switching frequency in response to said adjusting activity, wherein said second marginal change is in opposition to said first marginal change.
 8. A method as claimed in claim 1 wherein: said method additionally comprises: generating a reference frequency; and comparing said switching frequency to said reference frequency; and said forming activity forms said variable window in response to said comparing activity.
 9. A method as claimed in claim 1 additionally comprising: generating pulses at a rate that defines a frequency at which said switching circuit switches said N switches; and distributing said pulses sequentially among said N switches.
 10. A method as claimed in claim 1 additionally comprising: distributing said stream of switching pulses sequentially among said N switches; detecting a transient; and redistributing at least one of said switching pulses to a different one of said N switches in response to said detecting activity.
 11. A method as claimed in claim 1 wherein said switching activity comprises distributing each of said switching pulses sequentially among said N switches.
 12. A method as claimed in claim 1 wherein said switching activity comprises: switching said N switches collectively at a substantially constant switching frequency; and frequency; and switching said N switches individually at N⁻¹ times said substantially constant switching frequency.
 13. A fixed-frequency switching power supply having N phases, where N is a positive integer, said power supply comprising: N switches configured to be coupled to a bipolar power source; N inductances, wherein each of said N inductances is coupled to one of said N switches; a capacitance coupled to each of said N inductances and configured to be coupled across a load; a feedback-signal generator coupled to said capacitance and configured to generate a comprehensive feedback signal in response to no more than two state variables of said power supply; a pulse-width-modulation (PWM) generator coupled to said comprehensive feedback-signal generator and configured to translate said feedback signal into a stream of switching pulses at a substantially constant switching frequency; and a phase selector coupled to said N switches, coupled to said PWM generator, and configured to switch said N switches at said substantially constant switching frequency in response to said stream of switching pulses so that each of said N switches effects one of said N phases.
 14. A power supply as claimed in claim 13 wherein said power supply additionally comprises: a monitor circuit configured to monitor an output voltage of said power supply; and a first state-variable generator coupled to said monitor circuit and configured to generate a first one of said two state variables as a difference between said output voltage and a fixed reference voltage equal to an idealized output voltage of said power supply.
 15. A power supply as claimed in claim 14 additionally comprising a second state variable generator coupled to said first state-variable generator and configured to synthesize a second one of said two state variables as a derivative of said first state variable over time.
 16. A power supply as claimed in claim 13 wherein said feedback-signal generator comprises a sliding-surface generator configured to generate said comprehensive feedback signal as a single sliding surface for said N phases.
 17. A power supply as claimed in claim 16 wherein said sliding surface has a value αx₁+x₂, where: α is a constant having a value greater than zero; x₁ is a first one of said two state variables; and x₂ is a second one of said two state variables.
 18. A power supply as claimed in claim 17 wherein said constant has a range, 0≦α≦(τ)⁻¹, where τ is a time constant having a value RC, where R is a value of a resistive component said load; and C is a value of said capacitance.
 19. A power supply as claimed in claim 17 wherein: said first state variable has a value V_(Ref)−V_(Out), where V_(Ref) is a value of a reference voltage, and V_(Out) is a value of an output voltage of said power supply; and said second state variable is a derivative of said first state variable over time.
 20. A power supply as claimed in claim 13 wherein: said power supply additionally comprises an inductive current generator configured to synthesize N synthesized inductive currents from said first state variable; and said PWM generator comprises a current-balance control coupled to said feedback signal generator, coupled to said inductive current generator, and configured to adjust said comprehensive feedback signal so that N inductive currents are rendered substantially equal in response to said N synthesized inductive currents, wherein each of said N inductive currents is a current through one of said N inductances.
 21. A power supply as claimed in claim 13 wherein: said load exhibits a change producing a first marginal change in said switching frequency; and said PWM generator produces a second marginal change in said switching frequency in opposition to said first marginal change.
 22. A power supply as claimed in claim 13 wherein: said PWM generator comprises a constant-frequency control comprising: a reference generator configured to generate a reference frequency; a frequency comparator coupled to said reference generator and configured to compare said switching frequency to said reference frequency; and said constant-frequency control maintains said switching frequency substantially constant in response to said frequency comparator.
 23. A power supply as claimed in claim 13 wherein: said feedback-signal generator is configured to generate a sliding surface; and said PWM generator is configured to form a variable window for said sliding surface.
 24. A power supply as claimed in claim 23 wherein said phase selector is configured to switch said N switches at said switching frequency, wherein said switching frequency is determined by said variable window.
 25. A power supply as claimed in claim 24 wherein said PWM generator forms said variable window so that said frequency is maintained substantially constant in response to load changes.
 26. A power supply as claimed in claim 23 wherein said Phase selector switches said N switches at said switching frequency, wherein said switching frequency is determined by said variable window and said load.
 27. A power supply as claimed in claim 26 wherein: said load exhibits a change producing a first marginal change in said switching frequency; and said constant-frequency control adjusts said variable window to produce a second marginal change in said switching frequency in opposition to said first marginal change.
 28. A power supply as claimed in claim 13 additionally comprising a transient control coupled to said PWM generator, coupled to said phase selector, configured to detect an occurrence of a transient in said power supply, and to redistribute one of said switching pulses to a different one of said N switches upon said occurrence.
 29. A power supply as claimed in claim 13 wherein: said phase selector collectively switches said N switches at said substantially constant switching frequency; and said phase selector individually switches each of said N switches at substantially N⁻¹ times said substantially constant switching frequency.
 30. A fixed-frequency multiphase sliding-mode switching power supply having N phases, where N is an integer greater than one, said power supply comprising: N switches configured to be coupled to a bipolar power source, wherein each of said N switches effects one of said N phases; N inductances, wherein each of said N inductances is coupled to one of said N switches; a capacitance coupled to each of said N inductances and configured to be coupled across a load; a constant-frequency control coupled to said sliding-surface generator, configured to form a variable window for said single sliding surface, and configured to translate said sliding surface into a stream of switching pulses at a substantially constant switching frequency in response to said sliding surface and said variable window; and a switching circuit coupled to said N switches, coupled to said constant-frequency control, and configured to switch said N switches at said substantially constant switching frequency in response to said stream of switching pulses.
 31. A power supply as claimed in claim 30 wherein: said constant-frequency control comprises a reference generator configured to generate a reference frequency; said constant-frequency control additionally comprises a frequency comparator configured to compare said switching frequency to said reference frequency; and said constant-frequency control adjusts said variable window in response to said frequency comparator to maintain said switching frequency substantially constant.
 32. A power supply as claimed in claim 30 wherein said switching frequency is determined by said variable window and said load.
 33. A power supply as claimed in claim 32 wherein: said load exhibits a change producing a first marginal change in said switching frequency; and said constant-frequency control adjusts said variable window to produce a second marginal change in said switching frequency in opposition to said first marginal change.
 34. A power supply as claimed in claim 30 wherein: said constant-frequency control is included in a pulse width modulation generator and is configured to generate pulses at a rate that defines said switching frequency; said switching circuit sequentially distributes pulses generated by said constant-frequency control to said N switches.
 35. A power supply as claimed in claim 34 additionally comprising a transient control coupled to said constant-frequency control, and configured to detect when a transient occurs and to redistribute a pulse to a different one of said N switches when said transient occurs.
 36. A system comprising: a bipolar power source configured to supply direct-current electrical energy in a first form; an electronic device configured to utilize direct-current electrical energy in a second form; and a sliding-mode switching power supply having N phases, where N is a positive integer, coupled between said bipolar power source and said electronic device, and configured to convert said direct-current electrical energy in said first form into said direct-current electrical energy in said second form, wherein said power supply comprises: N switches coupled to said bipolar power source, wherein each of said N switches effects one of said N phases; N inductances, wherein each of said N inductances is coupled to one of said N switches; a capacitance coupled to said N inductances and said electronic device; a feedback-signal generator configured to generate a comprehensive feedback signal for said N phases; a pulse-width-modulation (PWM) generator comprising: a translation circuit coupled to said feedback-signal generator and configured to translate said feedback signal into a stream of switching pulses at a substantially constant switching frequency; and a phase selector coupled to said N switches, coupled to said PWM generator, and configured to sequentially switch said N switches at said substantially constant switching frequency in response to said stream of switching pulses.
 37. A system as claimed in claim 36 wherein said electronic device is one of a computing device and a communications device.
 38. A system as claimed in claim 36 wherein: said feedback-signal generator comprises a sliding-surface generator configured to generate a single sliding surface for said N phases as said feedback signal.
 39. A system as claimed in claim 38 wherein: said translation circuit is a constant-frequency control comprising: a reference generator configured to generate a reference frequency; a frequency comparator configured to compare said switching frequency to said reference frequency to produce a frequency error; and a variable-window generator configured to form a variable window for said sliding surface in response to said error frequency.
 40. A system as claimed in claim 39 wherein: said switching circuit switches said N switches in response to said sliding surface, said variable window, and an impedance of said electronic device; said electronic device exhibits a change in said impedance, wherein said change in said impedance produces a first marginal change in said switching frequency; and said constant-frequency control adjusts said variable window and produces a second marginal change in said switching frequency in opposition to said first marginal change. 